SPE 142884 A Unified Mathematical Model for Unconventional Reservoir Simulation

Unconventional hydrocarbon resources from low-permeability formation, i.e., tight sands and shales, are currently received great attention because of their potential to supply the entire world with sufficient energy for the decades to come. In the past few years, as a result of industry-wide R&D effort, progresses are being made towards commercial development of gas and oil from such unconventional resources. However, studies, understandings, and effective technologies needed for development of unconventional reservoirs are far behind the industry needs. Unconventional reservoir dynamics is characterized by highly nonlinear behavior of multiphase flow in extremely lowpermeability rock, coupled by many co-existing, processes, e.g., non-Darcy flow and rock-fluid interaction within tiny pores or micro-fractures. Quantitative characterization of unconventional reservoirs has been a significant scientific challenge currently. Because of complicated flow behavior, strong interaction between fluid and rock as well as multi-scaled heterogeneity, the traditional Darcy-law-and-REV-based model may not be applicable for describing flow phenomena in unconventional reservoirs. In this paper, we will discuss a general mathematical model proposed for unconventional reservoir simulation. We will present a unified framework model to incorporate various nonlinear flow and transport processes using a multi-domain, multi-continuum concept to handle multi-scaled heterogeneity of unconventional formation. Specifically, we will use extended or modified Darcy law to include the following processes: (1) non-Darcy flow with inertial effects; (2) non-Newtonian behavior (i.e., threshold pressure gradient for flow to occur); (3) adsorption and other reaction effect; and (4) rock deformation. The proposed modeling methodology has been implemented into a general reservoir simulator and will be demonstrated for its application in analyzing well tests in fractured vuggy reservoirs, non-Darcy flow, and non-Newtonian flow in porous and fractured reservoirs. Introduction Significant progress has been made in the past decade in producing gas and oil from unconventional petroleum resources, including low-permeability shale oil and gas reservoirs, and tight gas formations. However, low gas/oil recovery rate from such unconventional resources remains as the main technical difficulty. For example, gas recovery rate from these unconventional resources is estimated at 10-30% of GIP, much lower from conventional gas reservoirs. Gas and oil production or flow in such extremely low-permeability formations is complicated by flow condition and many co-existing processes, such as severe heterogeneity, Klinkenberg effect (Klinkenberg, 1941), non-Darcy flow behavior, adsorption/desorption, strong interactions between fluids (gas and water) molecules and solid materials within tiny pores, as well as microand macrofractures of shale and tight formations. Currently, there is little in basic understanding on how these complicated flow behavior impacts on gas flow and the ultimate gas recovery from such reservoirs. There is a general lack in technologies or approaches available for effective gas production from unconventional reservoirs (MIT, 2010), except two technologies: horizontal drilling and hydraulic fracturing, which seems to work (Denny, 2008; Bybee, 2008; King, 2010). In particular, there are no effective and applicable reservoir